Question

Assume that according to the official rules of an international sport, a ball acceptable for tournament play must bounce to a height of between 175 and 185 cm when dropped from a height of 254 cm at room temperature. What is the acceptable range of values for the coefficient of restitution for the ball-floor system?

Answer 1

Answer:0.829 to 0.853

Explanation:

Given

height through ball is dropped $h=254 cm$

velocity at just before collision is $u=\sqrt{2gh}$

$u=\sqrt{2\time 9.8\times 2.54}$

$u=7.05 m/s$

if the now if the ball rises to a height of 175 cm , velocity after collision to reach at that height is

$v_a=\sqrt{2\times 9.8\times 1.75}=5.85 m/s$

if the ball rises to an height of 185 cm then velocity after collision

$v_b=\sqrt{2\times 9.8\times 1.85}=6.02 m/s$

value of e for $h=175 cm$

$e=\frac{5.85}{7.05}$

$e=0.829$

e for 185 cm

$e=\frac{6.02}{7.05}=0.853$

Range of e is 0.829 to 0.853